Scilab Function
Last update : September 1997

oldbesseli - Modified Bessel functions of the first kind (I sub alpha).

oldbesselj - Bessel functions of the first kind (J sub alpha).

oldbesselk - Modified Bessel functions of the second kind (K sub alpha).

oldbessely - Bessel functions of the second kind (Y sub alpha).

Calling Sequence

y = oldbesseli(alpha,x)
y = oldbesseli(alpha,x,ice)
y = oldbesselj(alpha,x)
y = oldbesselj(alpha,x,ice)
y = oldbesselk(alpha,x)
y = oldbesselk(alpha,x,ice)
y = oldbessely(alpha,x)
y = oldbessely(alpha,x,ice)

Parameters

Description

these functions are obsolete, use besseli, besselj, besselk, bessely instead. Note however that the semantics of these two functions are different.

oldbesseli(alpha,x) computes modified Bessel functions of the first kind (I sub alpha), for real, non-negative order alpha and real argument x. oldbesseli(alpha,x,2) computes oldbesseli(alpha,x).*exp(-abs(real(x))).

oldbesselj(alpha,x) computes Bessel functions of the first kind (J sub alpha), for real, non-negative order alpha and real argument x. oldbesselj(alpha,x,2) computes oldbesselj(alpha,x).*exp(-abs(imag(x))).

oldbesselk(alpha,x) computes modified Bessel functions of the second kind (K sub alpha), for real, non-negative order alpha and real argument x. oldbesselk(alpha,x,1) computes oldbesselk(alpha,x).*exp(x)

oldbessely(alpha,x) computes Bessel functions of the second kind (Y sub alpha), for real, non-negative order alpha and real argument x. oldbessely(alpha,x,1) computes oldbessely(alpha,x).*exp(-abs(imag(x))).

alpha and x may be vectors. The output is m-by-n with m = size(x,'*'), n = size(alpha,'*') whose (i,j) entry is oldbesseli(alpha(j),x(i)).

I_alpha and K_alpha are 2 independant solutions of the modified Bessel's differential equation :


          2                     2        2
         x  y(x)" + x y(x)' - (x  + alpha ) y(x) = 0 , 
     
    

J_alpha and Y_alpha are 2 independant solutions of the Bessel's differential equation :


          2                     2        2
         x  y(x)" + x y(x)' + (x  - alpha ) y(x) = 0 , 
     
    

Examples


// example : display some I bessel functions
x = linspace(0.01,10,5000)';
y = oldbesseli(0:4,x);
ys = oldbesseli(0:4,x,2);
xbasc()
subplot(2,1,1)
   plot2d(x,y, style=2:6, leg="I0@I1@I2@I3@I4", rect=[0,0,6,10])
   xtitle("Some modified bessel functions of the first kind")
subplot(2,1,2)
   plot2d(x,ys, style=2:6, leg="I0s@I1s@I2s@I3s@I4s", rect=[0,0,6,1])
   xtitle("Some modified scaled bessel functions of the first kind")
 
  

Author

W. J. Cody, L. Stoltz (code from Netlib (specfun))